Method and apparatus for measuring pH of low alkalinity solutions

ABSTRACT

Systems and methods are described for measuring pH of low alkalinity samples. The present invention provides a sensor array comprising a plurality of pH indicators, each indicator having a different indicator concentration. A calibration function is generated by applying the sensor array to a sample solution having a known pH such that pH responses from each indicator are simultaneously recorded versus indicator concentration for each indicator. Once calibrated, the sensor array is applied to low alkalinity samples having unknown pH. Results from each pH indicator are then compared to the calibration function, and fitting functions are extrapolated to obtain the actual pH of the low alkalinity sample.

BACKGROUND OF THE INVENTION

1. Field of Invention

The present invention relates generally to a system for measuring pH,and more particularly relates to an improved method and apparatus formeasuring pH of low alkalinity solutions by extrapolatingspectrophotometric measurements from a plurality of pH indicatorsensors.

2. Description of Related Art

A wide variety of systems and methods have been employed for pHmeasurement of water systems. For example, a glass electrode is commonlyused for pH measurement in both a laboratory and industrial environment.Alternatively, it is known that spectrophotometric techniques may beused for pH measurement. Exemplary systems and methods for pHmeasurement have been described in U.S. patent application Ser. No.11/507,689 filed Aug. 22, 2006, which is assigned to the same assigneeas the present application, the disclosure of which is herebyincorporated by reference herein.

While the prior art devices and systems have provided useful products,they have not been entirely satisfactory in providing a fast, simple,and accurate measurement of low alkalinity water samples in a relativelysimple and user friendly manner. One of the challenges associated withmeasuring pH of low alkalinity solutions is that perturbation in pHinduced by introduction of indicators into the sample solution is notnegligible. This is true because indicators themselves are weak acids orbases. Stated another way, the pH of a weakly buffered (i.e., lowalkalinity) solution can be severely perturbed due to the fact that theamount of indicator concentration introduced into the sample issignificant in relation to the quantity of acid or base in the solution.

Prior art attempts have been made to minimize or correct for indicatorinduced perturbation in aqueous phase by: (1) adjusting the pH of theindicator stock solution close to the pH of the samples; (2) decreasingthe ratio of indicator addition to the sample volume; and (3) observingindicator induced pH perturbations through stepwise indicator additions,and then using linear extrapolation methods to obtain the pH of thesample. Such prior art methods may provide useful results, but they aretypically very time consuming and non-user-friendly. Therefore, a strongneed remains for an improved method and system that provides a precise,accurate, and fast pH measurement for low alkalinity samples in arelatively cost effective and user-friendly manner.

SUMMARY OF THE INVENTION

One of the challenges associated with measuring pH of low alkalinitysolutions is that perturbation in pH values induced by the introductionof indicators into the sample solutions is not negligible. As a result,pH measurements can be severely perturbed due indicator concentrationsbeing introduced into a weakly buffered (i.e., low alkalinity) solution.To meet this challenge, the present invention discloses systems andmethods comprising a sensor array comprising a plurality of pHindicators, each indicator having a different indicator concentration.The sensor array is calibrated by applying the sensor array to a samplesolution having a known pH. The response from each pH indicator issimultaneously recorded, and a calibration function (i.e., calibrationcurve) is generated representing the pH response versus indicatorconcentration for each indicator concentration. Once calibrated, thesensor array may then be applied to low alkalinity sample solutionshaving unknown pH. Results from the pH values from each pH indicator arecompared to the calibration curve, and a fitting function (i.e., fittingequations) representing the pH response from each indicatorconcentration is generated. Fitting equations are then generated andextrapolated to determine the intercept points (i.e., when indicatorconcentration is zero) to obtain the original (i.e., actual) pH of theunknown sample.

Other aspects of the present invention relate to the use of such systemsand methods, and to exemplary methods for measuring pH of low alkalinitysolutions. Further aspects of the present invention and its advantagesover the prior art will become apparent upon reading the followingdetailed description and the appended claims with reference to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graphical illustration showing changes in pH afterintroduction of various amounts of thymal blue;

FIG. 2 depicts a series of plots showing pH values of differentsolutions before and after indicator addition;

FIG. 3 is a graph illustrating the relationship between pH measuredversus the amount of phenol red added;

FIG. 4 illustrates calibration curves generated on four distinctindicator concentrations;

FIG. 5 is a graph illustrating a result from an exemplary linearextrapolation method of the present invention;

FIG. 6 depicts a pH sensor array in accordance with an exemplaryembodiment of the present invention;

FIG. 7 depicts a single use or disposable test array card in accordancewith an exemplary embodiment of the present invention; and

FIG. 8 depicts a fluidic delivery device that can be used with the testarray card of FIG. 7.

DETAILED DESCRIPTION OF INVENTION

The present invention describes systems and methods comprising a polymerfilm-based sensor array for quickly and accurately measuring pH of lowalkalinity solutions, for example low alkalinity water samples. It isknown that alkalinity or buffer capacity is one of the basic features ofwater samples. Alkalinity is a measure of the ability of a solution toneutralize acids. A lower alkalinity means lower capacity to resist thechange to pH when an acid is added to the solution.

The concept of the present invention is based on the recognition that inlow alkalinity solutions, perturbation of pH induced by introduction ofindicators into the sample is not negligible. This is true becauseindicators themselves are weak acids or bases. As a result, pH of asolution can be severely perturbed due to the fact that the amount ofindicator concentration introduced into the sample is significant inrelation to the quantity of acid or base present in the weakly buffered(i.e., low alkalinity) solution. This perturbation effect is even morepronounced in pH indicator loaded film.

To meet this challenge, one aspect of the present invention describes anextrapolation process for quickly and accurately measuring pH of lowalkalinity samples. The method preferably utilizes, but is not limitedto, a sensor array constructed in accordance with U.S. patentapplication Ser. No. 11/507,689 earlier incorporated by referenceherein. Such sensor array is configured to comprise a plurality ofindicator portions, each with different indicator concentrations. Onceconstructed, the sensor array is used to spectrophotometrically measurepH of the sample, whereby each indicator provides a discrete absorbancepH measurement simultaneously. The measured pH values from eachindicator portion are plotted versus their respective indicatorconcentrations, and a fitting function (i.e., fitting equation)representing the measured pH values is extrapolated to determine theintercept points when indicator concentration is zero to obtain theinitial pH (i.e., pH real) of the sample. The systems and methods of thepresent invention provide advantage over known methods because insteadof trying to minimize pH perturbations caused by indicator additions,the present invention exploits the relationship between pH perturbationsfrom different indicator concentrations to calibrate the sensor array,thus providing a baseline reference parameter for determining pHmeasurements from low alkalinity samples having unknown pH.

As disclosed herein, the systems and methods of the present inventionare particularly well suited for quickly and accurately determining pHof low alkalinity solutions. Measuring pH of low alkalinity solutions isnot trivial due to perturbations induced by the addition of weak acidsor base indicators into the solution, especially when the indicatorconcentration (which is typically either a weak acid or base) issignificant in relation to the quantity of acid or base in the samplesolution. pH response may be measured by calorimeter, spectrophotometer,or fluorescent spectrometer.

In accordance with an exemplary embodiment of the present invention, apH sensor array was constructed with a four-film array, although it isunderstood that more or less films could be used without departing fromthe scope of the present invention. Each sensor film contained adifferent pH indicator concentration which will be denoted as In₁, In₂,In₃, and In₄ respectively. For purposes of the examples herein, theindicator concentration of each film ranged from about 0.01 to 10%.

The solid films are typically prepared from water-soluble polymers,cellulose acetate, or Poly 2-Hydroxyethyl Methacrylate (pHEMA). Theindicators may be colorimetric pH indicators, fluorescent pH indicators,or other suitable pH indicators known or later developed in the art.Colorimetric pH indicators are preferably selected from a groupconsisting of phenol red, cresol red, m-cresol purple, thymol blue,bromochlorophenol blue W.S., bromocresol green, chlorophenol red,bromocresol purple, bromothymol blue, neutral red, phenolphthalein,o-cresolphthalein, nile blue A, thymolphthalein, bromophenol blue,metacresol purple, malachite green, brilliant green, crystal violet,methyl green, methyl violet 2B, picric acid, naphthol yellow S, metanilyellow, basic fuchsin, phloxine B. methyl yellow, methyl orange,alizarin.

To demonstrate the concepts of the present invention, we carried out atheoretic calculation of pH change (i.e., perturbation) to lowalkalinity solutions due to the addition of differing amounts ofindicator material into a sample solution. Although the examplesdisclosed herein are included to demonstrate the broad applicability ofthe present invention, it should be appreciated by those of skill in theart that the techniques disclosed in the examples herein representtechniques discovered by the inventors, and thus can be considered toconstitute exemplary modes for its practice. However, those of skill inthe art should, in light of the present disclosure, appreciate that manychanges can be made in the specific embodiments which are disclosed andstill obtain a like or similar result without departing from the scopeof the invention. And the calibration and extrapolation methodsdisclosed herein may be used to determine pH of low alkalinity sampleswith pH responses measured by colorimeter, spectrophotometer, orfluorescent spectrometer.

A shown in FIG. 1, a graphical illustration shows how changes in pH arerealized after introduction of various amounts of thymal blue into thesolution. The results of FIG. 1 indicate that the delta pH (i.e., pHreal-pH measured) becomes bigger and bigger with increasing additions ofindicator concentration into the solution. This result clearlyillustrates that weakly buffered (i.e., low alkalinity) solutions can beseverely perturbed by indicator additions.

With continued reference to FIG. 1, theoretic calculation of pHperturbation demonstrates that the lower the alkalinity is, the biggerthe delta pH is. Therefore, we can draw the conclusion that with moreaddition of indicator, and with lower alkalinity, the greater the pH ofthe solution will be changed or perturbed.

To prove this conclusion, we conducted a first experiment in which aseries of 100 ppm carbonate buffers were implemented, and the pH valueof different solutions was measured before and after indicatoradditions. Results from this first experiment are shown in FIG. 2. Asshown in FIG. 2, a series of plots illustrates pH values of differentsolutions measured before and after indicator additions. Based on theseresults, it is apparent that when 20 ppm phenol red (acid form) wasadded to the solution, the pH measurement slightly decreased. FIG. 2also illustrates that a gradual decrease of the pH was observed as theamount of phenol red increased from 0 ppm (diamond points) to 100 ppm(square points). When more phenol red 100 ppm was added, the pH wasgreatly perturbed. As shown by FIG. 2, with 100 ppm phenol red added,solutions with pH higher than about 8.0 became essentiallyindistinguishable. Based on these results, it became apparent that acorrection on delta pH induced by indicator additions could be accountedfor to obtain the actual pH (pH real) of the solution.

Accordingly, we conducted a second experiment to show that anextrapolation method may be useful to determine pH. In this secondexperiment, two 100 ppm carbonate buffers with original pH of 8.12 and8.53 were chosen. Indicator phenol red which has a pH response rangefrom about 6.8 to 8.2 was used. When an acid form of phenol red wasadded stepwise to the weakly buffered carbonate solution, a pH meter wasused to monitor the pH of the solution.

As shown in FIG. 3, a linear relationship of pH measured to the 100 ppmindicator addition was plotted for each of the 100 ppm carbonatebuffers. The linear functions representing pH measured from eachindicator type were extrapolated when indicator percentage was zero toobtain the intercept points. As shown in FIG. 3, the intercept points,namely 8.13 and 8.46, represent pH of the solution when indicatorconcentration is zero. In this way, the intercept points represent theoriginal pH of the solution before indicator additions. It is readilyapparent that the intercept points are very close to the initial pHvalues, i.e., 8.12 and 8.53, of the carbonate buffers, respectively.Consequently, our experiment demonstrates that pH perturbation due toindicator condition is not negligible when alkalinity is very low.Moreover, our experiment demonstrates that the exemplary linearextrapolation technique of the present invention is quite useful toobtain the sample's original pH. The algorithms used in the exemplaryextrapolation technique are described in more detail below.

To correct for changes in pH induced by indicator additions, acalibration curve was set up using a synthetic cooling standard solutionwith high enough alkalinity versus solid pH sensor with a series ofindicator concentrations. In this third experiment, the pH of sampleswas measured with the same solid pH sensor, and the pH measured for eachindicator concentration was calculated. The pH measured versus indicatorconcentration was then plotted and a fitting equation was generated andextrapolated when indicator concentration is zero to obtain the initialpH (i.e., pH real) of the unknown sample.

As shown in FIG. 4, a calibration curve was generated on four (0.5%,1.0%, 1.5%, 2.0%) indicator concentrations. The pH value of an unknownsample with low alkalinity (less than 100 ppm) was measured.

FIG. 5 is a graph illustrating results from an exemplary linearextrapolation method of the present invention. As can be seen from FIG.5, the intercept point of the equation (i.e., when indicatorconcentration is zero) is 9.18. Since the intercept point represents pHbefore indicator additions, our extrapolation method demonstrates thatthe intercept point of 9.18 is a very good approximation to the actualpH value 9.07 measured by a pH meter.

In order to achieve the results illustrated in FIGS. 4 and 5, a pHsensor array was constructed with a four-film array in which each sensorfilm contained a different pH indicator concentration, as In₁, In₂, In₃,and In₄ respectively. Next, an absorbance response was measured for eachpH sensor film from a series of pH standard solutions having a fixed andknown alkalinity value.

Next, a calibration curve was generated for each pH sensor film from thedata measured from the previous second step. The calibration functionsare denoted f₁, f₂, f₃, and f₄ for purposes of the calculations shownbelow.

Next, an unknown pH sample was applied to the pH sensor array, andabsorbance values measured from each film. For purposes of calculationsshown below, these absorbance values are denoted A₁, A₂, A₃, and A₄ forfilms 1, 2, 3, and 4 respectively.

Next, preliminary pH values are calculated for each film from eachcorresponding calibration equation and absorbance value. For example, pHfor films 1-4 are represented as: pH₁=f₁(A₁), pH₂=f₂(A₂), pH₃=f₃(A₃),and pH₄=f₄(A₄), respectively. It is noted that these pH values would allbe the same if the alkalinity value of the unknown sample is equal tothat of the calibration standard solution. However, pH₁, pH₂, pH₃, andpH₄ will all have different values if the alkalinity value of theunknown sample is not equal to that of the calibration standardsolution.

In the final step, the actual pH value for the unknown sample iscalculated from the preliminary pH values pH₁, pH₂, pH₃, and pH₄ basedon the extrapolation algorithm given below:

$\begin{matrix}{{pH}_{sample} = \frac{\begin{matrix}{\sum\left( {In}_{i}^{2} \right)} & {\sum\left( {{In}_{i}*{pH}_{i}} \right)} \\{\sum{In}_{i}} & {\sum{pH}_{i}}\end{matrix}}{\begin{matrix}{\sum\left( {In}_{i}^{2} \right)} & {\sum{In}_{i}} \\{\sum{In}_{i}} & N\end{matrix}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$where:

-   i is the film index;-   In_(i) stands for the indicator concentration in the i^(th) film;-   pH_(i) is the apparent pH value calculated from absorbance of the    i^(th) film and the corresponding calibration equation f_(i);-   and N is number of pH films.

FIG. 5 is a graphic illustration of the exemplary extrapolationalgorithm. Calculations for the results shown in FIG. 5 and thecorresponding mathematic procedure are shown below:N=4, i=1, 2, 3, and 4  Equation 2:Σ(In _(i))²=2.02+1.52+1.02+0.52=7.5  Equation 3:ΣpH _(i)=8.38+8.60+8.75+9.00=34.73  Equation 4:ΣIn _(i)=2.0+1.5+1.0+0.5=5.0  Equation 5:ΣIn _(i) ·pH _(i)=2.0×8.38+1.5×8.60+1.0×8.75+0.5×9.00=42.91  Equation 6:pH sample=(34.73×7.5−5.0×42.9)/(7.5×4−5.0×5.0)=9.18  Equation 7:

Based on the results describe above, the present invention thus providesa system for directly measuring the pH of low alkalinity samples byproviding a sensor array having a plurality of indicator concentrations,and calibrating the pH measured of an unknown sample to the calibrationcurve generated from a known sample to obtain the pH of the unknownsample. In accordance with the present invention, these measurements arerecorded simultaneously in a timely manner to avoid the tedious andlengthy measurements and calculations involved with stepwise indicatoradditions. As an example, an exemplary solid film sensor of the presentinvention demonstrated a rapid response to the target, with resultsbeing obtained within about five minutes for in situ (on field) tests.

As described herein, the systems and methods of the present inventionincorporate a solid polymer-based pH sensor film array comprising aseries of different indicator concentrations. Once constructed, thesensor array is applied to a sample solution containing a known pH andalkalinity. The pH response from each indicator concentration issimultaneously measured and recorded. Next, a calibration function(i.e., calibration curve) is generated by plotting the pH measuredversus each indicator concentration. The calibration curve thusrepresents a plot of the pH measured versus indicator concentration.Next, a fitting function (i.e., fitting equation) representing each pHmeasurement is generated. The fitting equation is extrapolated todetermine the intercept points when indicator concentration is zero,thus obtaining an accurate indication of the original pH of the samplebefore indicator additions. In this way, the calibration curverepresents a baseline reference function which can be used to calibratethe discrete results from each indicator portion to quickly and easilyexploit the perturbation of pH from different indicator additions so asto extrapolate the pH of low alkalinity samples.

FIG. 6 depicts a pH sensor array in accordance with an exemplaryembodiment of this invention. The array 10 transports a controlledamount of a liquid sample, in metered quantities, to multiple reservoirs8 in order to effect a chemical reaction between the sample fluid andthe sensor elements (not shown) connected to the reservoirs 8. As shownin FIG. 6, the array 10 comprises a top cover layer 2, a middle channellayer 4, a bottom sampler-substrate binding (i.e., gasket) layer 6, afluid entry port 12, and an associated plastic entry port wall ring 11.A plurality of grooves or channels 5 are formed on the channel layer 4for directing the sample fluid from the fluid entry port 12 to thereservoirs 8. A plurality of channels is formed when the cover layer 2is bound to the channel layer 4. A series of vent holes 7 are added toassure complete fluid flow through the channel system. Due to thecapillary force driving the fluid through the channels 5, no pumps andvalves are required to deliver a given amount of liquid sample orreagent from the sample entry port 12 to the multiple reservoirs 8within a predefined sequence.

FIG. 7 illustrates a single-use or disposable test array card 9, alsoreferred to as a disk or substrate, comprising diverse chemically orphysically responsive sensor films 3 in accordance with an exemplaryembodiment of the present invention. The sensor films 3 can be groupedinto chemical or physically similar sets of one or more films dependingon the desired fidelity of a sensor response through the use of outlierelimination or statistically processing of the individual filmresponses.

FIG. 8 illustrates a fluidic delivery device 10 that can be aligned andassembled to the test array card 9 using the locating holes 1. Thedelivery device 10 transports a controlled amount of a liquid sampleinjected at the entry port 12, in metered quantities, to an array ofreservoirs 8 through channels 5 radiating out of the entry port 12 tothe reservoirs 8 in order to effect a chemical reaction between thesample fluid and the sensor element 3 connected to the cell. In additionthe fluidic delivery device provides four sidewalls and the roof of thereservoirs with the test array card 9 providing the bottom floor. Theroof of the reservoirs comprises a film that has circular vent holes 7that vent air out of the reservoirs as they are filled with sampleliquid. The vent hole material, diameter and depth are optimized toregulate the effective venting of air and containment of sample fluidwithin the controlled dimensions of walls of the reservoirs 8.

While the disclosure has been illustrated and described in typicalexemplary embodiments, it is not intended to be limited to the detailsshown, since various modifications and substitutions can be made withoutdeparting in any way from the scope and spirit of the presentdisclosure. As such, further modifications and equivalents of thedisclosure herein disclosed may occur to persons skilled in the artusing no more than routine experimentation, and all such modificationsand equivalents are believed to be within the scope of the disclosure asdefined by the following claims.

1. A method for measuring pH of a low alkalinity sample solution,comprising the steps of: providing a pH sensor array having a pluralityof pH indicator films, each said pH indicator film having a differentindicator-concentration; applying said sensor array to a series of pHstandard solutions having fixed and known pH and alkalinity values;simultaneously measuring a pH response for each pH indicator film ofsaid sensor array; generating a calibration equation for each pHindicator film that provides the apparent pH as a function of said pHresponse, said calibration equations are generated using said pHresponses for each pH indicator film from said series of pH standardsolutions; applying said sensor array to a low alkalinity samplesolution having an unknown pH and an alkalinity of less than 100 ppm;calculating preliminary pH values for each film from each correspondingcalibration equation and pH response using the equation:pH _(i) =f _(i)(A _(i)) where: i is the pH indicator film index, f_(i)is the calibration equation that provides the apparent pH value as afunction of pH response for the i^(th) pH indicator film, A_(i) is themeasured pH response for the i^(th) pH indicator film, pH_(i) is theapparent pH value calculated from the measured pH response of the i^(th)pH indicator film and the corresponding calibration equation;calculating the actual pH value for the low alkalinity sample solutionusing the extrapolation equation: ${pH}_{sample} = \frac{\begin{matrix}{\sum\left( {In}_{i}^{2} \right)} & {\sum\left( {{In}_{i}*{pH}_{i}} \right)} \\{\sum{In}_{i}} & {\sum{pH}_{i}}\end{matrix}}{\begin{matrix}{\sum\left( {In}_{i}^{2} \right)} & {\sum{In}_{i}} \\{\sum{In}_{i}} & N\end{matrix}}$ where: i is the index corresponding to each pHindicator; In_(i) is the indicator concentration of the i^(th)indicator; pH_(i) the apparent pH value calculated from the pH responseof the i^(th) pH indicator film and the corresponding calibration curve;and N is number of pH indicators.
 2. The method of claim 1, wherein saidindicators are solid polymer based, pH indicator-containing films. 3.The method of claim 2, wherein said indicators are colorimetric pHindicators or fluorescent pH indicators.
 4. The method of claim 3,wherein said colorimetric pH indicators are selected from the groupconsisting of phenol red, cresol red, m-cresol purple, thymol blue,bromochlorophenol blue W.S., bromocresol green, chlorophenol red,bromocresol purple, bromothymol blue, neutral red, phenolphthalein,o-cresolphthalein, nile blue A, thymolphthalein, bromophenol blue,metacresol purple, malachite green, brilliant green, crystal violet,methyl green, methyl violet 2B, picric acid, naphthol yellow S, metanilyellow, basic fuchsin, phloxine B, methyl yellow, methyl orange,alizarin.
 5. The method of claim 1, wherein said pH response is measuredby colorimeter, spectrophotometer, or fluorescent spectrometer.
 6. Themethod of claim 2, wherein said solid films are prepared fromwater-soluble polymers.
 7. The method of claim 2, wherein said solidfilms are prepared from Poly 2-Hydroxyethyl Methacrylate (pHEMA) orcellulose acetate.
 8. The method of claim 2, wherein said sensor arraycomprises at least four pH indicators having concentrations on the orderof about 0.01% to 10%.
 9. The method of claim 1, further comprising thestep of generating graphical representations of said calibrationequations and preliminary pH values.
 10. A method for measuring pH of alow alkalinity sample solution, comprising the steps of: providing a pHsensor array having at least four solid polymer based pHindicator-containing films, each said pH indicator film having adifferent concentration of phenol red; applying said sensor array to aseries of pH standard solutions having fixed and known pH and alkalinityvalues; simultaneously measuring a pH response for each pH indicatorfilm of said sensor array; generating a calibration equation for each pHindicator film that provides the apparent pH as a function of said pHresponse, said calibration equations are generated using said pHresponses for each pH indicator film from said series of pH standardsolutions; applying said sensor array to a low alkalinity samplesolution having an unknown pH and an alkalinity of less than 100 ppm;calculating preliminary pH values for each film from each correspondingcalibration equation and pH response using the equation:pH _(i) =f _(i)(A _(i)) where: i is the pH indicator film index, f_(i)is the calibration equation that provides the apparent pH value as afunction of pH response for the i^(th) pH indicator film, A_(i) is themeasured pH response for the i^(th) pH indicator film, pH_(i) is theapparent pH value calculated from the measured pH response of the i^(th)pH indicator film and the corresponding calibration equation;calculating the actual pH value for the low alkalinity sample solutionusing the extrapolation equation:${p\; H_{sample}} = \frac{\begin{matrix}{\sum\left( {In}_{i}^{2} \right)} & {\sum\left( {{In}_{i}*p\; H_{i}} \right)} \\{\sum{In}_{i}} & {\sum{p\; H_{i}}}\end{matrix}}{\begin{matrix}{\sum\left( {In}_{i}^{2} \right)} & {\sum{In}_{i}} \\{\sum{In}_{i}} & N\end{matrix}}$ where: i is the index corresponding to each pHindicator; In_(i) is the indicator concentration of the i^(th)indicator; pH_(i) the apparent pH value calculated from the pH responseof the i^(th) pH indicator film and the corresponding calibration curve;and N is number of pH indicators.
 11. The method of claim 10, whereinsaid solid films are prepared from water-soluble polymers.
 12. Themethod of claim 10, wherein said solid films are prepared from Poly2-Hydroxyethyl Methacrylate (pHEMA) or cellulose acetate.
 13. The methodof claim 10, wherein said sensor array pH indicators have concentrationson the order of about 0.01% to 10%.
 14. The method of claim 10, furthercomprising the step of generating graphical representations of saidcalibration equations and preliminary pH values.